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Mass vs. Weight: Accelerating Mass

To demonstrate Newton's Second Law of Motion, astronauts on the International Space Station use force as provided by the spring in a tape measure to act on objects of varying mass. Their demonstration shows that bodies with greater mass are accelerated less by the same force.

This media asset is from the Mass vs. Weight series produced by the Teaching From Space Office at NASA's Johnson Space Center.

Mass In normal conversation, when we use the word “massive” we’re usually referring to how big something is. Scientifically speaking, though, “mass” isn’t related to size (or volume). Mass is related to how much an object resists changes to its state of motion. Though it’s true that, for a given density, more volume will mean more mass, some objects can be “small” - in the sense that they don’t take up a lot of volume - yet still have a lot of mass. (One example would be the dense material that makes up a neutron star.) Conversely, large objects can have low mass. Think about a mountain of granite versus a mountain of cotton candy. Both might have the same volume, but they have different masses. (And one tastes better, too.) An object with more mass requires more effort – more force - to get moving from a state of rest, or to stop once it’s in motion. That quality of being easy or hard to set in motion or bring to a stop is “inertia.” An object’s “inertial mass” is its resistance to being accelerated (or decelerated) by a force.

Gravitational Force All masses near Planet Earth feel a gravitational force proportional to their mass: the bigger the mass, the bigger the gravitational force. The equation for gravitational force is: FG = Mass x Gravity = mg. The value of “g” (the strength of the gravitational field) is unique to each planet. While g here on Earth may be ~10 m/s2, on Jupiter, g ~25 m/s2 and on the Moon, g is only ~ 1.6 m/s2. And since the value of g changes based on the gravitational field strength, the gravitational force also changes. Neither an object’s state of motion nor its specific location impacts gravitational force. What matters is the value of g.

Weight Gravitational force is associated with acceleration in the direction of that force. Simply put, an object subject to a gravitation force will “fall” in the same direction in which the force is acting. The force it takes to counteract and balance out that falling is the object’s “weight.” Unlike mass and unlike gravitational force, weight will change based on whether there are forces acting that increase or reduce the “upward” force necessary to balance out the “downward” gravitational force; for instance the buoyant force that helps an object float in water, making it weightless.

Another example of an object’s weight changing is due to it’s acceleration relative to the gravitational field. If an object is pushed upwards so that it accelerates up, it’s weight on the surface pushing it up will increase. Alternatively, if the object is allowed to fall, it’s weight will be reduced. For example, when you’re in an elevator, going over the top of a steep bump in your car or riding a roller coaster, your weight changes because you are experiencing an upward or downward acceleration, so your weight does not completely offset the gravitational force. In each scenario, your weight is the net force required to counteract the downward force such that you experience a certain acceleration, and that value can change even though the gravitational force remains the same.

Weightlessness When astronauts are in the space station, their mass is the same as it is on Earth. The gravitational force on the space station - contrary to what many people think – is only slightly less than the gravitational force on Earth. The space station, and everything in it, is subject to Earth’s gravity. Indeed, that’s what keeps it in orbit. However, since the station and everything on it moves together around Earth, the space station and its contents are constantly falling towards Earth; they are in free fall. They never fall to Earth, since the curvature of Earth exactly matches the shape of the orbit, but they are constantly falling, nonetheless. The station and its contents are weightless since no force is exerted to counterbalance the gravitational force. Based on what it means for something to have weight, this explains why – despite having mass and despite being subject to a gravitational force – the astronauts are weightless. The condition of weightlessness on board the space station allows astronauts to conduct experiments and demonstrations that would be impossible to do on Earth.

Imagine two sealed plastic bags that are exactly the same - except one bag is empty and one bag is filled with water. On Earth, one would weigh more than the other, right? (Which one - and why?) Now imagine taking both bags into space, where, for all intents and purposes, neither has any weight – yet the two bags are still different, aren’t they? How would you describe the differences?

If you had two similar-looking bricks on a table, and you knew one was made of concrete and the other was made of Styrofoam, how could you tell which was which without lifting or weighing the bricks?

Imagine a tee-ball set-up in which you swing a bat each time with the same force. If you hit a solid wooden sphere and then a hollow plastic sphere with the same force, will the different spheres react differently? If so, how?

While Viewing

In this demonstration, what provides the force that accelerates the masses?

Tip: Stop the video at the split-screen image showing the time comparison between the empty bag and full bag. Have students write down the time results for the first two experiments. Ask students what those times correspond to and what those results tell us about the two different water bags and their masses.

Tip: Stop the video again at the designated pause point. Ask students to make a prediction about what will happen when one of the astronauts becomes the test mass. Will he accelerate at a higher or lower rate than the water bags? Ask them to explain how they arrived at their predictions. Possible prompt if needed: Ask students how the astronaut’s mass compares to the previous two test masses – the empty and filled water bags. Then ask if they think the answer to that question might help them form a prediction. Resume video to see the results.

What was the result of the third experiment? How did that result compare to the first two?

After Viewing

Why did the empty bag accelerate more rapidly than the full bag?

Amongst all three test masses, why did the astronaut have the lowest rate of acceleration?

Why was it important to test objects of different mass?

Which bag was moving faster by the time it was finished going 1 meter? How do you know?

Put the three test objects in order based on mass. In a separate column, put them in order based on the time results from the experiments in the video. What do you notice when you compare the two lists? How do you think the results relate to each object’s rate of acceleration? (Background note: Since the masses begin with a speed of zero, the time they take to cover the distance is inversely proportional to their respective rates of acceleration. If one or more of the objects had had an initial speed, the force still would have caused the objects to accelerate, but we wouldn’t have been able to use the time results for comparisons.)

Imagine a new object that has a hundred times more mass than the astronaut. If you could test this new object using the same force that was used in the other experiments, would it accelerate? If so, do you think it would accelerate more quickly or more slowly than then other objects did? If you think the new object wouldn’t accelerate at all, explain why not.

Bonus question: What would happen if you tried to set up the same experiment on Earth? Would the objects respond on Earth as they did in space? Wouldn’t the tape measure spring exert the same force whether in space or on the ground – and would that mean the results would be the same on Earth as in space? What other factors would you want to consider when comparing experimental results for Earth versus space?

Students work in small groups to explore the relationship between mass and acceleration for different car designs. Student groups research actual technical data for specific cars to find respective masses, or that information is provided for them. (Note: Chart can be developed and provided.)

Students work through several scenarios for different cars (different masses) to explore the relationship between mass and acceleration for a given force (example: 3500 N) and then graph their results to quantify the relationship.

Discussion Questions

Which car had the highest acceleration?

What factors do you think car designers take into account when designing cars for everyday use? What about when designing for race cars?

This design exercise isolated specific variables. What other factors do you think affect the relationship between mass and acceleration for different cars?

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